Render outputs includes the scene incorrectly or uses the wrong input
Since this was a very strange behaviour, I wanted to check the whole setup in the node editor.
I realised that it seems I was searching in the wrong part of the rendering pipeline. Somewhere I got the idea to look at the compositor window.

This is what I saw:


I have no idea how or why the setup was that way. It may was caused by the motion tracking workflow I did at the very start.

Since my only goal was to overlay the movie clip with the coloured objects, I deleted everything but the movie clip, the rendered scene and the alpha mixer (plus the two outputs of course).



With this configuration I got what I wanted and blender render did work as well for rendering.